Two similar cones have volumes 12π cu, units and96π cυ.units,the cu

1.	Two similar cones have volumes 12π cu, units and96π cυ.units,the curved surface area of the smaller cone is 15t sq units, what isthe curved surface area of the larger one?s
Answer» Let R = radius of base and L = lateral height, H = height of cone. curved surface or lateral surface = A = π R L , and volume = V = π/3* R² H, Similar cones have the same (cone) angle at the apex. Hence the same ratios among R, H and L. Let Cone 1 be the larger cone. Let R₂ = x R₁, H₂ = x H₁ and L₁ = x L₂ V₁ / V₂ = π R₁² H₁ / π R₂² H₂ = x³ = 96 π / 12 π = 8 Hence x = 2 Lateral Surface areas A₁ / A₂ = π R₁ L₁ / π R₂ L₂ = x² = 4 , as x = 2 A₁ = 4 A₂ = 4 * 15 π = 60 π square units.

Two similar cones have volumes 12π cu, units and96π cυ.units,the curved surface area of the smaller cone is 15t sq units, what isthe curved surface area of the larger one?s

Answer»

Let R = radius of base and L = lateral height, H = height of cone.

curved surface or lateral surface = A = π R L , and volume = V = π/3* R² H,

Similar cones have the same (cone) angle at the apex. Hence the same ratios among R, H and L. Let Cone 1 be the larger cone.

Let R₂ = x R₁, H₂ = x H₁ and L₁ = x L₂

V₁ / V₂ = π R₁² H₁ / π R₂² H₂ = x³ = 96 π / 12 π = 8

Hence x = 2

Lateral Surface areas A₁ / A₂ = π R₁ L₁ / π R₂ L₂ = x² = 4 , as x = 2

A₁ = 4 A₂ = 4 * 15 π = 60 π square units.